A splash in a one-dimensional cold gas

TL;DR

This paper investigates the dynamics of a one-dimensional cold gas with alternating particle masses, revealing shock formation, self-similar hydrodynamic behavior, and a ballistic splash region through analytical and molecular dynamics methods.

Contribution

It introduces a detailed analysis of shock and splash regions in a 1D cold gas with alternating masses, combining analytical solutions with simulations.

Findings

Shock front develops and moves sub-ballistically in the bulk.

A splash region of recoiled particles moves ballistically with negative velocities.

Hydrodynamic and non-hydrodynamic regimes coexist and are analytically characterized.

Abstract

We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, $m$ and $M$. The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by self-similar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations.